Exponential Function Evaluation

Consider an exponential function given by the equation:

$$f(x) = a imes b^x$$

where $a$ is a constant, $b$ is the base (where $b > 0$ and $b \neq 1$), and $x$ represents the independent variable. Suppose the function passes through the points $P(0, 4)$ and $Q(3, 32)$.

1. Determine the values of $a$ and $b$ based on the given points.

2. Using these values, calculate the value of $f(2)$.

Provide your answer as a decimal.